SOLUTION
Given the question, the following are the solution steps to answer the question.
STEP 1: Write the given system of equation
[tex]\begin{gathered} x+y=4----equation\text{ 1} \\ x-y=6-----equation\text{ 2} \end{gathered}[/tex]STEP 2: Solve the given equation
Subtract equation 2 from equation 1
[tex]\begin{gathered} (x-x)+(y-(-y))=4-6 \\ y+y=-2 \\ 2y=-2 \\ Divide\text{ both sides by 2} \\ \frac{2y}{2}=-\frac{2}{2} \\ y=-1 \end{gathered}[/tex]STEP 3: Solve for x
[tex]\begin{gathered} Substitute\text{ -1 for y in equation 1} \\ x+(-1)=4 \\ x-1=4 \\ x=4+1 \\ x=5 \end{gathered}[/tex]The values of x and y are 5 and -1 respectively meaning that the system has one solution, hence the type of system of equation given is a CONSISTENT system of linear equation.
Write an expression in simplest for the volume of the new cube in terms of a.
After decreasing the sidelength to 20% of the original size, the new sidelength is:
[tex]0.20a[/tex]The volume of a cube is given by the product of 3 of its sidelengths, it means, that the volume of the cube is the sidelength raised to 3:
[tex]V=(0.20a)^3=0.008a^3[/tex]The diameter D of a sphere is 13.6 mm calculate thr sphere volume Vuse the value 3.14 for pie, and around to the nearest 10th
Step 1
State the volume of a sphere
[tex]\begin{gathered} v=\frac{4}{3}\pi r^3 \\ \pi=3.14 \\ \frac{Diameter}{2}=\text{radius}=\frac{13.6}{2}=6.8\operatorname{mm} \end{gathered}[/tex]Step 2
Find the volume of the sphere by substitution of values.
[tex]\begin{gathered} v=\frac{4}{3}\times3.14\times(6.8)^3 \\ v=\frac{4}{3}\times3.14\times314.432 \\ v=1316.421973\operatorname{mm} \\ v\approx1316.4\operatorname{mm}^3\text{ to the nearest tenth} \end{gathered}[/tex]Hence, the volume of the sphere= 1316.4mm³ to the nearest tenth
Question in picture please answer I’ll give bonus points if right
Answer:
Division Property
Step-by-step explanation:
Step 3: 4x = -24
÷4 ÷4
---------------
Step 4: x = -6
Since -24 is being divided by 4 the division property is being used.
I hope this helps
A cellphone company offers two talk and text plans. The company charges a monthly service fee of $20 for either plan the customer chooses: Customers that choose Talk and Text Plan A are charged five cents a minute and twenty dollars for 250 texts. Customers that choose Talk and Text Plan B are charged ten cents a minute (first 100 minutes free) and fifteen dollars for 200 texts. The equation c = .10(m – 100) + 15 + 20 can be used to represent how much a customer would spend monthly for the minutes used. ** Express Plan A as an equation where c equals the cost and m equals the minutes used. a. Graph each Talk and Text plan to determine when both plans cost the same.
For question a), we have to write the equation of the cost (c) as a function of the minutes (m), so:
[tex]c_A=0.05\cdot m+20+20[/tex]In the equation above the term 0.05*m represent the 5 cents for minute then we have to sum the $20 for 250 texts and $20 of service fee.
Before we draw the lines, we can solve the question c). If a customer wants to spend $75 monthly we can recommen him the plan wich more minutes for that cost, so we need to calculate the minutes for each plan:
[tex]\begin{gathered} \text{For Plan A:} \\ c_A=75=0.05\cdot m+20+20 \\ 0.05\cdot m=75-20-20=35 \\ m=\frac{35}{0.05}=700 \\ \text{For Plan B:} \\ c_B=75=0.1\cdot(m-100)+15+20 \\ 0.1\cdot(m-100)=75-15-20=40 \\ m-100=\frac{40}{0.1}=400 \\ m=400+100=500 \end{gathered}[/tex]The customer should choose the Plan A, because it has more minutes and more texts for $75.
For point b), we can evaluate each equation in two differents m-values and found the pairs (m, c) to graph the lines, so:
[tex]\begin{gathered} \text{For Plan A, we can choose m=100 and m=500}\colon \\ m=100\Rightarrow c_{}=0.05\cdot100+20+20=45 \\ m=500\Rightarrow c=0.05\cdot500+20+20=65 \\ P_{1A}=(100,45),P_{2A}=(500,65) \end{gathered}[/tex][tex]\begin{gathered} \text{For Plan B, we can choose m=100 and m=500:} \\ m=100\Rightarrow c=0.1\cdot(100-100)+15+20=35 \\ m=500\Rightarrow c=0.1\cdot(500-100)+15+20=75 \\ P_{1B}=(100,35),P_{2B}=(500,75) \end{gathered}[/tex]And the graphs are:
In the Graphs we can see the lines intercept in m=300 and evluating the equations in that value the cost is $55.
The amount of time a certain brand of light bulb lasts is normally distributed with a
mean of 1300 hours and a standard deviation of 65 hours. What is the probability
that a randomly chosen light bulb will last between 1390 hours and 1460 hours, to the
nearest thousandth?
The probability that a randomly chosen light bulb will last between 1390 hours and 1460 hours is 3.1% to the nearest thousandth.
What is Normal Probability Distribution?In a normal distribution with mean and standard deviation, the z-score of a measure X is given by:
[tex]z = x - \mu/ \sigma[/tex]
The Z-score measures how many standard deviations the measure is from the mean.
In a set with mean and standard deviation , the z-score of a measure X is;
Mean of 1300 hours and a standard deviation of 65 hours.
This is the p-value of Z when X = 1460. So
[tex]z = x - \mu/ \sigma[/tex]
z = 1460 - 1300 /65
z = 1.87
Then has a p-value of 0.031.
0.031 = 3.1% is the probability that a randomly chosen light bulb will last between 1390 hours and 1460 hours, to the nearest thousandth.
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whats the middle of 130 - 170
Answer:
middle number is 150
Step-by-step explanation:
the middle of 130 - 170:
170 - 130 = 40
40/2 = 20
so the middle is:
130 + 20 = 150
or can be found:
170 - 20 = 150
middle number is 150
Answer:
150
Step-by-step explanation:
Add the two extreme numbers and take the average
130 + 170 = 300
300/2 = 150
150 is 20 distant from 130 and also 20 distant from 170
7.) Use the information to prove:
Given: The Diagram
Prove: EC AD
With the given information, we have proved that EC ≅ AD as corresponding sided of congruent triangles are congruent too.
What is congruent triangles?Both triangles are said to be congruent if the three angles and three sides of one triangle equal the corresponding angles and sides of the other triangle. We can see in the examples PQR and XYZ that PQ = XY, PR = XZ, and QR = YZ, and that P = X, Q = Y, and R = Z. Then, we can state that XYZ and PQR are related.
We have given that that ∠ADB = ∠ECB
And ∠ABC = ∠EBC as they are vertically opposite angles
And given that AB = EB
Thus, Triangle ABC ≅ Triangle EBC
And as ABC ≅ EBC
EC ≅ AD as corresponding sided of congruent triangles are congruent too.
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A motorcyclist starts his trip at noon and drives 10 miles in the first hour, and then in
each hour after that, he drives 6 more miles than in the previous hour.
After how many hours of driving will the motorcyclist drive a total of 248 miles?
After 248 miles, the motorcycle rider would have put in 40.6 hours of driving.
By using the arithmetic progression formula, we may find the answer to this problem.
The definition of arithmetic progressionA series of numbers in order known as an arithmetic progression has a constant value as the difference between any two consecutive numbers.
According to what we've been told, the first hour is separated by an arithmetic difference of six miles, or 10 miles. He covered a distance of 248 miles, according to the information we have. It follows that
An = a + (n-1)d, where
An = 248
a = 10
n = ?
d = 6
applying the formula, we have
248 = 10 + (n - 1)6
248 = 10 + 6n - 6
248 = 6n + 4
6n = 248 - 4
6n = 244
n = 244/6
n = 40.6 hours
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Solve for r.0.5(r +2.75) = 3
The given equation is,
[tex]0.5\mleft(r+2.75\mright)=3[/tex]To solve the above equation for r, first divide both sides of the equation by 0.5.
[tex]\begin{gathered} \frac{0.5\mleft(r+2.75\mright)}{0.5}=\frac{3}{0.5} \\ r+2.75=6 \end{gathered}[/tex]Subtract 2.75 from both sides of the above equation.
[tex]\begin{gathered} r+2.75-2.75=6-2.75 \\ r=3.25 \end{gathered}[/tex]Therefore, the value of r is 3.25.
3. On the map 1/3 cm represents 5 kilometers. How many centimeters on map represent 200 kilometers?A. 1/5B. 1 2/3C.13 1/3D. 40E. 66 2/3
Answer:
C.13 1/3 cm
Explanation:
On the map, 5km is represented by 1/3 cm.
Therefore:
[tex]1\operatorname{km}\text{ is represented by }\frac{1}{3}\div5=\frac{1}{15}cm[/tex]We can then conclude that:
[tex]\begin{gathered} 200\operatorname{km}\text{ is represented by }\frac{1}{15}\times200\text{ cm} \\ \frac{1}{15}\times200=13\frac{1}{3}cm \end{gathered}[/tex]The correct choice is C.
a car loses value at a rate of $2,500 per year (slope) you purchase a car for $21,000 which equation can be used to find y its value in dollars, x years after it was purchased
The value decreases at the rate of 2500 means slope of equation is -2500 and present value is 21000 so y intercept for the line is 21000.
Determine the equation for the car value after x years.
[tex]y=-2500x+21000[/tex]So answer is -2500x + 21000.
Tammy invested $2000 in a fund for 4 years and was paid simple interest. The total interest that she received on the investment was $400. As a percentage, what was the annual interest rate of her investment?
Answer:
Use this steps to find your answer
1. Provide a summary of the story “The Stone” Summarize the events in the exposition, rising action, climax, falling action, and resolution. Your written response should include 5 complete sentences.
Answer:
pls hurry
According to the plot synopsis for the novel "The Stone," a young homosexual guy experiences Taipei's nightlife, complete with all of its thrills and heartbreaks, perils, and hopes.
The Story of the Stone, sometimes referred to as "The Dream of the Red Chamber," was one of the finest books in Chinese literature when it was published about 1760. Gao E painstakingly edited and finished Cao Xueqin's majestic saga's fifth chapter, "The Dreamer Awakens," decades later.
The Story of the Stone has several references to or hints at the issue of the difference between what is true and what is untrue. The first volume in a five-volume series on the illustrious Chinese Jia family is titled "The Story of the Stone."
The major storyline chronicles the development of the love triangle between the three main characters—cousins Bao-yu, Dai-yu, and Bao-chai—as they grow up.
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(a)does the figure have reflectional symmetry? if so, give the n-fold number of the symmetry. (b)does the figure have rotational symmetry? if so, give the order and angle measure of the rotation.
(b) A figure is said to have an n-fold rotational symmetry if rotating through an angle of 360° / n does not change the figure.
In the case of the given figure, rotation through 180° does not change the figure.
Therefore,
[tex]\frac{360^o}{n}=\frac{180^o}{1}[/tex]Cross-multiplying, we have
[tex]\begin{gathered} 180^on=360^o \\ \text{ Dividing both sides by 180, we have} \\ n=\frac{360^o}{180^o}=2 \end{gathered}[/tex]Hence, the order of rotation is 2 and the angle is 180°
Evaluate the function at the given values.
H(r) = 8
a. H(3) = |
b. H (8) =
c. H (0)
A store owner buys sweatshirts for $16 and marks them up 20% to make a profit. The sales tax where his store is located is 7.5%. A customer considers buying one or two sweatshirts from the store. Select all the statements that apply.
A One sweatshirt before tax costs $19.20.
B One sweatshirt before tax costs $12.80.
C The sales tax for two sweatshirts is $1.92.
D The sales tax for two sweatshirts is $2.88.
E Total cost for two sweatshirts is $41.28
F Total cost for two sweatshirts is $27.52.
(you can only choose up to three btw)
The correct statement are;
⇒ One sweatshirt before tax costs $19.20.
Option A is true.
What is Percentage?
A relative value indicating hundredth part of any quantity is called percentage.
Given that;
Cost of sweatshirts for a store owner = $16
Profit percent = 20%
Sales tax = 7.5%
Now,
Profit price for a sweatshirts = 20% of $16
= 20/100 × 16
= 320 / 100
= $3.20
And, The sales tax price = 7.5% of 16
= 7.5 / 100 × 16
= 120 / 100
= $1.20
So, The cost of one sweatshirt before tax costs = $16 + $3.20
= $19.20
And, Sales tax for one sweatshirt = $1.20
So, Cost of sales tax for two sweatshirt = 2 × 1.20
= $2.40
And, Total cost of a sweatshirt = $16 + $3.20 + $1.20
= $20.4
So, Total cost of two sweatshirt = 2 × $20.4
= $40.8
Thus, The correct statement are;
⇒ One sweatshirt before tax costs $19.20.
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A family has two cars. The first car has a fuel efficiency of 35 miles per gallon of gas and the second has a fuel efficiency of 15 miles per gallon of gas. During one particular week, the two cars went a combined total of 1350 miles, for a total gas consumption of 50 gallons. How many gallons were consumed by each of the two cars that week?
First car:
Second car:
Answer:
Follow these steps to find your answer
take the square root of both sides of the equation from part B ( n↑2−c↑2=0 ) and write the resulting equation. how can this equation be true, and what does this show about the relationship between the two triangles?
SOLUTION
From the question and the instructions given,
Since
[tex]\begin{gathered} n^2-c^2=0 \\ square\text{ rooting both sides } \\ \sqrt{n^2}-\sqrt{c^2}=\sqrt{0} \\ square\text{ cancels square root, we have} \\ n-c=0 \end{gathered}[/tex]Thus, the triangles have all sides congruent, since the triangles are congruent.
Hence, this means that triangle 1 is a right triangle.
pleae help me and show work you will be braineist
The equation of a line is given by:
[tex]y-y_1=m(x-x_1)[/tex]where (x1,y1) is a point on the line and m is the slope. To find the slope of a line we use the formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]In this case, we have:
[tex]m=\frac{4-3}{5-(-2)}=\frac{1}{5+2}=\frac{1}{7}[/tex]Then, the equation of the line is:
[tex]\begin{gathered} y-4=\frac{1}{7}(x-5) \\ 7y-28=x-5 \\ x-7y=-23 \end{gathered}[/tex]Therefore:
[tex]x-7y=-23[/tex]Which expression is equivalent to9 30429O-49 20-13O4 301-(-3)O22COIN | ST
We must find the expression equivalent to:
[tex]\frac{-2\frac{1}{4}}{-\frac{2}{3}}.[/tex](1) The numerator is a mixed fraction, we can write it as a simple fraction:
[tex]\frac{-2\frac{1}{4}}{-\frac{2}{3}}=\frac{-2-\frac{1}{4}}{-\frac{2}{3}}=\frac{-\frac{8}{4}-\frac{1}{4}}{-\frac{2}{3}}=\frac{(-\frac{9}{4})}{(-\frac{2}{3})}.[/tex](2) Finally, we can rewrite the quotient between numerator and denominator using the symbol ÷, we get:
[tex]\frac{-2\frac{1}{4}}{-\frac{2}{3}}=\frac{(-\frac{9}{4})}{(-\frac{2}{3})}=(-\frac{9}{4})\div(-\frac{2}{3}).[/tex]Answer[tex](-\frac{9}{4})\div(-\frac{2}{3})[/tex]Kylie wants to ride her bicycle 27.5 miles this week. She has already ridden 9 miles. If she rides for 5 more days, which equation or tape diagram could be used to represent the context if mm represents the average number of miles she would have to ride to meet her goal?
The equation to represent the context is 9 + 5m = 27.5
How to frame the equation?
Number of miles Kylie wants to ride in a week= 27.5
Number of miles already ridden = 9
Average number of miles to meet her goal = mm
Let average no. of miles in 5 days = 5m
Rewriting as equation,
9 + 5m = 27.5
How to find the average number of miles?
5m = 37.5 -9
5m = 18.5
m = 18.5
[tex]m =\frac{18.5}{5} \\\\m = 3.7 \text{ or } 3\frac{7}{10}[/tex]
Kylie should travel 3.7 miles per day and 18.5 miles in 5 days to meet her goal
What is an equation?
A mathematical statement that has two expressions with equal values separated by the symbol ' = ' is called an equation. The expression on the left and the expression on the right are shown to be equal in reference to one another. The equations are solved to determine an unknown variable's value, which corresponds to an unknown quantity. It is not an equation if there is no equal to sign in the statement and shall be taken into account as an expression.To learn more about equations, refer:
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I need help making a tree diagram
Please don't close the session, the image its downloading
John recently joined a bowling team and each night plays three games. During his first two games he scored 112 and 134. What must John score on his last game to ensure his average for that night will be exactly 132?explain pls.
Let the score in his last game be
[tex]=x[/tex]The average of the three games is given as
[tex]=132[/tex]Step 1: The formula for average is
[tex]\text{average}=\text{ }\frac{\text{sum of the thre}e\text{ scores}}{3}[/tex]Step 2:Substituting the values of the three scores in the formula above, we will have
[tex]\begin{gathered} \text{average}=\text{ }\frac{\text{sum of the thre}e\text{ scores}}{3} \\ \text{average}=\frac{112+134+x}{3}=132 \end{gathered}[/tex]Step 3 : Cross multiply the equation below
[tex]\begin{gathered} \frac{112+134+x}{3}=\frac{132}{1} \\ \frac{246+x}{3}=\frac{132}{1} \\ 246+x=3\times132 \\ 246+x=396 \end{gathered}[/tex]Step 4: Subtract 246 from both sides
[tex]\begin{gathered} 246+x=396 \\ 246-246+x=396-246 \\ x=150 \end{gathered}[/tex]Hence,
John must score a point of 150 to ensure that his average is 132
Therefore,
Final answer = 150
1.5.PS-9Question HelpError Analysis Simplify the expression - 1.8+(-1.2). On the test, when Tom simplified theexpression he got 0.6. What mistake did Tom likely make when he simplified the expression?- 1.8+(-1.2) = 1 (Type an integer or a decimal.)
Answer:
-3.0
Explanation:
First, we open the bracket and take note that:
[tex]+\times-=-[/tex][tex]\begin{gathered} -1.8+\left(-1.2\right)=-1.8-1.2 \\ =-3.0 \end{gathered}[/tex]Next, we determine Tom's mistake.
[tex]\begin{gathered} 1.8+(-1.2)=1.8-1.2 \\ =0.6 \end{gathered}[/tex]Therefore, the mistake Tom made was that he ignored/forgot the negative sign before 1.8.
Decay (calculus problem)
Answer:
Step-by-step explanation:
If the half-life is k days, then you have
(1/2)^(300/k) = 0.696
k = 573.788
makes sense, since 69.6% is greater than 50%
Now solve for t in
(1/2)^(t/573.788) = 1/3
t = 909.432 days
makes sense -- about 1.5 half-lives
The table shows the changes in a city's average weekly temperature.
Week Average Temperature (ºF)
1 24.4
2 24.8
5 26.1
8 27.2
15 30.1
24 33.6
The data shows
trend.
Based on the table, we can assume that the city's average weekly temperature in the 26th week will
The city's average weekly temperature in the 26th week will be between 30.1 and 33.6 degrees be more than 33.6 degrees.
What is mean by linear expression?
A linear expression is an algebraic statement where each term is either a constant or a variable raised to the first power.
Given that;
The regression line shows slope of 0.4 and has y - intercept as 24.029.
Now,
Since, The slope is positive, we find that when week increase temperature as;
The regression equation will be;
y = 24.029 + 0.4x
For week = 26
y = 24.029 + 0.4x
y = 24.029 + 0.4 × 26
y = 24.029 + 10.4
y = 34.429
Which is greater than 33.6.
Thus, The city's average weekly temperature in the 26th week will be between 30.1 and 33.6 degrees be more than 33.6 degrees.
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The complete question is this;
The table shows the changes in a city's average weekly temperature. Week Average Temperature (ºF) 1 24.4 2 24.8 5 26.1 8 27.2 15 30.1 24 33.6. The data shows a positive linear a negative linear an exponential an unrecognizable trend. Based on the table, we can assume that the city's average weekly temperature in the 26th week will be between 30.1 and 33.6 degrees be more than 33.6 degrees be less than 33.6 degrees not change .
May I get help? I seem to keep losing connection
Answer
Option C is correct.
A = 1, B = 1, C = 0, D = -8, and E = 7
Explanation
The equation of a circle with center (h, k) and a radius of r, is given as
(x - h)² + (y - k)² = r²
This can then be expanded to form the general form of the equation,
Ax² + By² + Cx + Dy + E = 0
For this question, where the center of the circle lies on the y-axis, the coordinates of the center of that circle will be (0, p)
where p is the y-coordinate of the center of the circle.
(x - h)² + (y - k)² = r²
(h, k) = (0, p)
h = 0, k = p
r = 3 units
(x - 0)² + (y - p)² = 3²
x² + y² - 2py + p² = 9
x² + y² -2py + p² - 9 = 0
Comparing this with Ax² + By² + Cx + Dy + E = 0
A = 1
B = 1
C = 0
D = -2p
E = p² - 9
We can easily see that only Option C has C = 0 and matches the equation of the circle described in the question.
Hope this Helps!!!
Consider the function f(x)=2x2 + 7x-30What are the zeros of the function?
We have the following quadratic function:
[tex]f(x)=2x^2+7x-30[/tex]And we need to find its zeros i.e. the solutions to the equation:
[tex]2x^2+7x-30=0[/tex]Given a quadratic equation like the following:
[tex]ax^2+bx+c=0[/tex]Its solutions are given by the quadratic solving formula:
[tex]x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]In our case we have a=2, b=7 and c=-30. Then we get:
[tex]x=\frac{-7\pm\sqrt[]{7^2-4\cdot2\cdot(-30)}}{2\cdot2}=\frac{-7\pm\sqrt[]{49+240}}{4}=\frac{-7\pm\sqrt[]{289}}{4}[/tex]So we continue:
[tex]x=\frac{-7\pm\sqrt[]{289}}{4}=\frac{-7\pm17}{4}[/tex]So we have two solutions:
[tex]\begin{gathered} x_1=\frac{-7+17}{4}=\frac{10}{4}=2.5 \\ x_2=\frac{-7-17}{4}=-\frac{24}{4}=-6 \end{gathered}[/tex]Then the answers are -6 and 2.5.
Which is a description of the vertical shift of the function f(t)=3sec(t-pi/4)-2
The vertical shift of the given function is -2 or down 2. (Option D)
Here's why:
The function is given in a form of:
[tex]f(t)=a\sec (bx-c)+d[/tex]where d is the vertical shift. Since -2 is the value of d in the given function, then, -2 is the vertical shift.
A car left the warehouse at 3:00 P.M. The car traveled 62 miles by 4:00 P.M. The car continued traveling at the same average speed. How many miles, altogether, did the car travel by 9:45 P.M.? Round the final answer to the nearest whole number.
From 3 PM to 4 PM = 1 hour
Speed rate = distance / time
Distance = 62 miles
Replacing:
Speed = 62 / 1 = 62 miles per hour
By 9:45 PM
9:45 - 3 PM = 6 hours .45 minutes = 6.75 hours
Distance = Speed x time = 62 x 6.75 = 418.5 miles
